MathDB
points on a plane can be covered by open squares

Source: 1982 Polish MO Finals p4

February 25, 2020
combinatoricscombinatorial geometry

Problem Statement

On a plane is given a finite set of points. Prove that the points can be covered by open squares Q1,Q2,...,QnQ_1,Q_2,...,Q_n such that 1≤NjSj≤41 \le\frac{N_j}{S_j} \le 4 for j=1,...,n,j = 1,...,n, where NjN_j is the number of points from the set inside square QjQ_j and SjS_j is the area of QjQ_j.
Back to ProblemsView on AoPS